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Препринт

FAMILY OF GRAPH DECOMPOSITIONS AND ITS APPLICATIONS TO DATA ANALYSIS

A new decomposition approach to complex systems analysis is suggested. The conventional approach deals with the construction of a single, “the most correct”, decomposition of the considered system. Meanwhile the suggested approach is oriented to the construction of a family of decompositions, whose properties reveal some important meaningful features of the initial system. The expedience and applicability of the elaborated approach are illustrated by three well-known and important cases: automatic classification, political voting body and stock market. In these cases, the presented results cannot be obtained by other known methods. These examples confirm the advantages of the suggested approach.